Running summarizing tools on a new article

Abstract: A growing number of choice modelling studies estimate their models "in willingness-to-pay (WTP) space", yet often treat this as a different model that fits better (or worse) than "preference space", and misread what its parameters represent. This note brings together and makes precise insights that have mostly been stated only in scattered places, organising them around a single condition for two specifications to be the same model. WTP space is a reparameterisation, and with non-random coefficients the two spaces give identical likelihoods, WTP estimates and standard errors. With deterministic heterogeneity in cost sensitivity, or non-linearity, WTP must still be computed as a ratio of partial derivatives, although a simple normalisation recovers a directly estimated WTP at a reference point. With random heterogeneity, latent class models are equivalent in the two spaces, while other mixtures are equivalent only when the implied distributions match, as with full-covariance lognormals, and independence is not a neutral assumption.